Thin-walled Cylinder Research Articles

Full active counter-roller spinning for thin-walled cylinders: Macroscopic deformation mechanism, mesoscopic texture evolution, and forming performance strengthening

The reliability and lightweight of hydrogen high-pressure storage present pressing global challenges. The forming mechanism of a novel full active counter-roller spinning (FACRS) process for thin-walled cylinders is studied from the perspective of macro‑meso coupling. This innovative process holds promise as a replacement for conventional mandrel spinning, enabling enhanced integration of form and property in manufacturing hydrogen bottle liners. Employing optimal Latin hypercube sampling, a response surface model is constructed for forming consistency (λ) of inner and outer surfaces, yielding an optimal set of process parameters under the Hooke-Jeeves algorithm. The resulting spun parts exhibit a more balanced and superior performance. A macro‑meso gradual cross-scale coupling simulation methodology is proposed, revealing that the process is characterized by the initial aggregation and subsequent reinforcement of texture, culminating in the formation of a "soft" rotated cubic texture, which still faces impediments or diminishes the orientation of texture. It is demonstrated that the evolution of texture is the result of the interactive coordination of various slip systems. Furthermore, the FACRS experiments and performance tests indicate that while enhancing the axial and circumferential mechanical properties of the spun parts, it also reduces material anisotropy. The grain refinement effect of the process has also led to a more uniform distribution of dimples on the fracture surface. The surface performance of the final spun parts improves by 60.11 %. These enhancements can be attributed to the combined effects of improved forming consistency, coordinated action of slip systems, and grain refinement. These results deepen the understanding of the macro‑meso deformation mechanisms underlying the novel process, providing valuable insights for further advancements in counter-roller spinning technology.

Easy-to-use formulations based on the homogenization theory for vascular stent design and mechanical characterization

Background and objectivesVascular stents are scaffolding structures implanted in the vessels of patients with obstructive disease. Stents are typically designed as cylindrical lattice structures characterized by the periodic repetition of unit cells. Their design, including geometry and material characteristics, influences their mechanical performance and, consequently, the clinical outcomes. Computational optimization frameworks have proven to be effective in assisting the design phase of vascular stents, facilitating the achievement of enhanced mechanical performances. However, the reliance on time-consuming simulations and the challenge of automating the design process limit the number of design evaluations and reduce optimization efficiency. In this context, a rapid and automated method for the mechanical characterization of vascular stents is presented, taking the stent geometry, conceived as the periodic repetition of a unit cell, and material as input and providing the mechanical response of the stent as output. MethodsVascular stents were assumed to be thin-walled hollow cylinders sharing the same macroscopic geometrical characteristics as the cylindrical lattice structure but composed of an anisotropic homogenized material. Homogenization theory was applied to average the microscopic inhomogeneities at the stent unit cell level into a homogenized material at the macro-scale, enabling the calculation of the associated homogenized material tensor. Analytical formulations were derived to relate the stent mechanical behavior to the homogenized stiffness tensor, considering linear elastic theory for thin-walled hollow cylinders and three loading scenarios of relevance for vascular stents: radial crimping; axial traction; torsion. Validation was conducted by comparing the derived analytical formulations with results obtained from finite element analyses on typical stent designs. ResultsHomogenized stiffness tensors were computed for the unit cells of three stent designs, revealing insights into their mechanical performance, including whether they exhibit auxetic behavior. The derived analytical formulations were successfully validated with finite element analyses, yielding low relative differences in the computed values of foreshortening, radial, axial and torsional stiffnesses for all three stents. ConclusionsThe proposed method offers a rapid, fully automated procedure that facilitates the assessment of the mechanical behavior of vascular stents and is suitable for effective integration into computational optimization frameworks.

Modeling of residual stiffness phenomenon in modified Iwan model of bolted joints and its application

Bolted joints have been widely used in various mechanical structures. Due to the presence of contact interfaces, the joints exhibit complex nonlinear behavior under dynamic loading. Effective prediction of the dynamic response of bolted structures requires the construction of appropriate dynamic models. This paper proposes a modified Iwan model which gives a more comprehensive description of joints than the previous Iwan models, especially for the phenomenon of residual stiffness in macro slip. The equations of the model's backbone curve, hysteresis curve, and energy dissipation are derived. The parameter identification procedure is also provided. Subsequently, connection elements based on the modified Iwan model are integrated into a single bolted joint and a thin-walled cylinder containing multiple bolted joints, the responses under quasi-static unidirectional loading, quasi-static cyclic loading and constant-frequency excitation are investigated. The physical interpretation of the parameters in the model is discussed, thus explaining the relationship between the bolted joint's physical parameters and some important variables. The results indicate that the model can effectively characterize the nonlinear mechanical behavior of the bolted joint for both micro and macro slip regime, with significant improvement in computational efficiency.

A case study: anti-corrosion performances of plasma sprayed AT13 coatings on CrZrCu thin wall cylinder with adjusted parameters for controlling deformation

PurposeThis paper aims to control the deformation of a thin wall CrZrCu cylinder components (wall thickness 5 mm, diameter 400 mm) during thermal spray alumina-titania (AT13) coating by adjusting the spray parameters without deteriorating its quality evidently.Design/methodology/approachThe deformation was controlled by lowering the temperature of the component in the way of adjusting the spray parameters. The main parameters adjust included extending the spraying distance, from normally 120 mm to 140 mm, decreasing plasma power from 50to 42 kW. An alumina-titanium (AT13) ceramic coating was chosen for protecting the substrate from corrosion. Microscopic morphology and phase analysis, insulation resistance testing, neutral salt test and electrochemical method were used to analyze the anti-corrosion and insulation performances of the coating.FindingsThe results indicate that, after adjusting the spraying parameters, the coating has a relatively high porosity, with an average value of 8.96 ± 0.77%. The bonding strength of the coating is relatively low, with an average value of 17.69 ± 0.85 MPa. However, after sealing, the polarization resistance of the coating in seawater can be maintained above 6.25 × 106 Ω.cm2 for an extended period. The coating has a high resistance (=1.1 M Ω), and there is no apparent galvanic corrosion when contacted with TC4 alloy. Additionally, analysis of corrosion products on the sample surface reveals that the samples with sprayed alumina-titanium ceramic show no copper corrosion products on the surface, and the coating remains intact, effectively isolating the corrosive medium.Originality/valueBy adjusting the spraying parameters, the deformation of the cylinder thin-walled component can be effectively controlled, making the φ 400 × 392 mm (thickness 5 mm) CrZrCu cylinder com-ponent with a maximum diameter deformation of only 0.14 mm. The satisfactory corrosion performances can be achieved under adjusting spraying parameters, which can guarantee the application of ceramic coating for weapon launching system of naval ships.

Simultaneous measurement of the distributed longitudinal strain and velocity field for a cantilevered cylinder exposed to turbulent cross flow

The structural response of a cantilevered cylinder under free-stream conditions both with low and high turbulence intensity generated by turbulence-generating grids is analysed with concurrent measurements of the velocity field and the distributed strain. The thin-walled cylinder, with a diameter (D) of 50 mm, is mounted in a water flume as a cantilevered beam supported at one end, with 95% of its body submerged and exposed to cross flow yielding a Reynolds number of Re = 25000. We employ a novel combination of simultaneous particle image velocimetry and distributed strain measurements using Rayleigh backscattering fibre optic sensors. These sensors are embedded onto the surface of the cylinder to measure the experienced strain (ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon $$\\end{document}) of the structure along its spanwise direction, covering both the windward and leeward faces of the cylinder. The sensors fine spatial resolution allows us to discern the influence of the flow on the structural response of the cylinder in two distinct regions of the structure: upstream and downstream of the mean separation location. This differentiation allows us to isolate the local effects introduced by the free-stream conditions on the loading events over the body from the global force generated by the vortex shedding and other coherent motions present within the flow. Distinguishing between these direct and indirect effects helps determine which is more relevant for fatigue-life cycle analysis. The cross power spectral density between the fluctuating velocity field and the strain reveals that the load is dominated by the vortex shedding, and this relationship is intensified with the introduction of free-stream turbulence. It also helps to discern the different dynamics imposed by the two free-stream turbulence conditions.

Expansion deformation mechanism and cracking behaviours of chromium-coated zirconium alloy cladding at room temperature

The deformation of the cladding tube triggered by the expansion of the internal plug is used to investigate the hoop deformation behaviour of the Cr-coated zirconium alloy cladding tube at room temperature. A thin-walled pressurized cylinder model is used to transform the axial load-displacement curve working on the expansion plug into the hoop stress-strain curve working on the cladding tube, and it is found that the Cr coating can be able to restrain the cladding tube from hoop deformation. Observation of the Cr-coated cladding tube after different amounts of hoop deformation revealed that the strain corresponding to the generation of the first crack was a ranged from 0.48 % to 0.59 %, the density of cracks started to grow very fast and then entered a saturation stage. The fracture strength of the Cr coating and maximum interfacial shear strength when the Cr coating crack density reaches saturation were calculated by the shear-lag model. Twins and a large number of dislocations were generated in the Zr matrix and a small number of dislocations in the Cr coating after the hoop deformation. The behaviour of crack initiation and propagation occurring in Cr coating is revealed.

AC losses in macroscopic thin-walled superconducting cylinders

Measurements of the ac response represent a valuable method for probing the properties of superconductors. In the surface superconducting state (SSS), a current exceeding the surface critical current I c leads to breakdown of SSS and penetration of external magnetic field into the sample bulk. An interesting free-of-bulk system in SSS is offered by thin-walled cylinders. According to the full penetration of magnetic flux (FPMF) model, each time the instant value of an ac field is equal to a certain critical value, the ac susceptibility χ will exhibit jumps as a function of the ac field amplitude H ac because of the periodic destruction and restoration of SSS in the cylinder wall. Here we study the low-frequency (128–8192 Hz) ac response of thin-walled niobium cylinders under superimposed dc and ac magnetic fields applied parallel to the cylinder axis. In contrast to the FPMF model predictions, experiments reveal a smooth χ(H ac) dependence. To explain the experimental observations, we propose a phenomenological partial penetration magnetic flux (PPMF) model, which assumes that after restoration of the superconducting state, the magnetic fields inside and outside the cylinder are unequal and the magnitude of the penetrating flux is random for every penetration. This model fits very well the experimental data on the temperature dependence of the first harmonic χ 1 for any dc field and ac amplitude.

The Behavior of Thin-Walled Cylinders with Ribs Regarding the Energy Absorption Capability on High-Velocity Impact

Many industries and automotive companies use thin-walled cylinders as energy-absorbing devices. Researchers have previously investigated various parameters related to thin-walled cylinders and their behavior under impact loads. When the impactor hits the thin-walled cylinder from the axial direction, it causes the bending of the cylinder wall on an axisymmetric or non-axisymmetric pattern, depending on the ratio of diameter divided by wall thickness. In addition, the length of the specimen influences the deformation mode that occurs. This study discusses how installing ribs on the cylinder walls affects energy absorption capabilities. We conducted the research by making modeling based on the finite element method by making various specimens according to the experimental scenarios. We experimented with an aluminum alloy cylinder with a diameter of 50 cm, a thickness of 1.5 mm, and a length of 200 mm. Then, successively, we installed ribs with a length of 2 mm and a thickness of 3.5 mm, one rib, two ribs, three ribs, four ribs, and five ribs. The impactor hits the specimen from the axial direction to one end at high speed while the other is given fixed support. The results obtained from the experiment are total deformation, reaction force, absorbed energy, and deformation pattern. The experimental results show that adding ribs changes the deformation pattern from previously non-axis-symmetric to axis-symmetric. The total deformation decreases, the reaction force becomes smaller, and the ability to absorb energy equals the total kinetic energy. This result is a recommendation for manufacturing in an energy absorption structural system. Keywords: rib, deformation mode, wall thickness, energy absorption, reaction force.

A Ground-Based Electrostatically Suspended Accelerometer.

In this study, we have developed an electrostatically suspended accelerometer (ESA) specifically designed for ground use. To ensure sufficient overload capacity and minimize noise resulting from high suspension voltage, we introduced a proof mass design featuring a hollow, thin-walled cylinder with a thin flange fixed at the center, offering the highest surface-area-to-mass ratio compared to various typical proof mass structures. Preload voltage is directly applied to the proof mass via a golden wire, effectively reducing the maximum supply voltage for suspension. The arrangement of suspension electrodes, offering five degrees of freedom and minimizing cross-talk, was designed to prioritize simplicity and maximize the utilization of electrode area for suspension purposes. The displacement detection and electrostatic suspension force were accurately modeled based on the structure. A controller incorporating an inverse winding mechanism was developed and simulated using Simulink. The simulation results unequivocally demonstrate the successful completion of the stable initial levitation process and suspension under ±1g overload.

Study on buckling of thin-walled composite cylinder under C-SS boundary condition

Study on buckling of thin-walled composite cylinder under C-SS boundary condition

Time-varying vibration characteristics and surface topography of thin-walled cylinders during machining operations

Machining thin-walled cylindrical workpieces is frequently subjected to vibration due to their low rigidity, resulting in complicated surface topography. This paper investigates the vibration characteristics of thin-walled cylinder turning as well as its effect on the machined surface topography comprehensively by means of numerical simulations and experimental measurements. It is seen that the circumferential shell mode of vibration exhibits higher sensitivity to the variation of the wall thickness than the axial beam mode. The features of the vibration characteristics as well as the machined surface textures of thin-walled workpieces are shifting in a cutting pass. The underlying physical mechanism behind this phenomenon was interpreted. By extracting the critical vibration frequency and surface waviness measurement along the cutting path, a hybrid physics and data-driven surface topography was reconstructed, which showed consistency with the real surface topography. The formulated correlation between the vibration characteristics and the surface topography contributes to a holistic understanding of dynamic behaviors of thin-walled cylinder machining, and a tool that utilizes vibration to produce functional microstructures on cylindrical surfaces.

Study on Dynamic Post-Buckling Stability of Thin-Walled Cylinders Subjected to Horizontal Vibration

Abstract As a lesson learned from the Fukushima nuclear accident, the importance of accident mitigation for beyond design basis events (BDBEs) is recognized. Excessive earthquake is a typical BDBE. During such events, the fast reactor main vessel (FRMV) is vulnerable to buckling because of its thin-walled cylindrical structure. Buckling deformation without causing immediate collapse should not be considered as a limit state in BDBEs. Instead, the objective is to achieve a stable post-buckling state. In the present study, dynamic post-buckling behavior of thin-walled cylinders under intense horizontal vibration is experimentally studied, which simulates loop-type FRMV design. Finite element method (FEM) simulation is also conducted and validated by experimental data. Based on results analysis, a global response stability after buckling is confirmed. The buckled model shows resilience to withstand catastrophic collapse even when intense excitation continues to apply. Using equivalent linear response method, dynamic mechanisms behind the stability are revealed. Due to substantial degradation of structural stiffness, the post-buckling response shifts into the out-of-phase domain such that response divergence is prevented. Meanwhile, the response is notably delayed from the input, which impedes the conversion of input energy into kinetic energy, reducing the inertial impact to the structure. These mechanisms are found to be independent of input waveforms and can be applied to a general seismic scenario. Moreover, the limit for global response stability after buckling and the effect of input frequency on the post-buckling behavior are clarified.

Enhancing radial strain uniformity of thin-walled cylinder by the dual asymmetric active counter-roller spinning process

Aiming at the problem of uneven forces on the inner and outer surfaces during counter-roller spinning (CRS) of thin-walled cylinders, which affects the spinning stability and forming quality, a new dual asymmetric active counter-roller spinning (DAACRS) process is proposed. It enhances the radial strain uniformity through more consistent contact of the inner and outer rollers and the material flow on the inner and outer surfaces. The theoretical analytical model of the influence of the spinning structural and process parameters on the contact condition and the oriented relationship is established. On this basis, the Kriging predictive surrogate model under the coupling influence of these parameters is established, and the spinning parameters optimized by the multi-objective particle swarm optimization (MOPSO) algorithm in the global continuous variables are obtained. The radial strain gradient effect of traditional spun parts is basically eliminated under this process parameters. Additionally, an active counter-roller spinning (ACRS) machine is independently developed and a comprehensive macro-micro quality evaluation method is proposed. The ACRS process can transform the material from dispersed {001}<110> low-strength plate texture to more standard {001}<100> high-strength plate texture, and obtain balanced axial and circumferential tensile strengths. Moreover, the new DAACRS process resulted in more balanced forming accuracy, inner and outer surface grain size, texture strength, and isotropic mechanical properties due to the high radial strain uniformity. Compared with the traditional completely symmetric active counter-roller spinning (CSACRS), the L̅, O̅, UD, UT{100}, UT{110}, and UT{111} are improved by 0.08265 mm, 0.00335 mm, 4.83%, 10.55%, 11.54%, and 16.34%, respectively. Further analysis provides that the allowable values of strain uniformity for the higher quality thin-walled cylinders are [Uε(PEEQ)]=0.365 and [Uε(Max Principal)]=0.438. These results increase the understanding of the strain change, microstructure evolution, and mechanical properties change mechanism of the CRS process, thereby providing important guidance for improving the CRS process and forming quality.

Finite-Element Modeling of the Dynamic Behavior of a Crack-like Defect in an Internally Pressurized Thin-Walled Steel Cylinder

This article presents one part of a study on the dynamic deformation and fracture of sections of steel gas pipelines with an external crack-like defect under the action of internal pressure. This work was performed on the basis of finite-element simulations using a cylindrical shell model executed by ANSYS-19.2 on the example of the section of the steel gas pipeline “Beineu–Bozoy–Shymkent” in the Republic of Kazakhstan. The propagation of the incipient crack-like defect along the pipeline and the resulting dynamic fracture in its tip area were investigated. The options of pipeline loading by working and critical internal pressure were both considered. It was found that, within the time of 1.0 ms, the formed crack expanded in the circumferential direction up to the maximum value, which depended on the value of the internal pressure. A further growth of cracks occurred along the longitudinal direction. At the operating pressure, the initial length of the crack increased by a factor of 5.6, while the equivalent stresses increased by a factor of 1.53 within 3.5 ms. Within the time of 3.75 ms, the equivalent stresses stopped growing due to the gas decompression. Specifically, there was a stop to the crack growth along the longitudinal direction. Vice versa, at the maximum pressure, the pipeline fracture did not change qualitatively, while at the time of the process, it decreased up to 3.5 ms. The finite-element results of the stress–strain state and pipeline fracture in the crack tip area at the working pressure showed that, within the time of 1.0 ms, the distance between the crack walls reached 23 mm at the free edge. Conversely, within the time periods of 2.25 and 3.5 ms, it increased two and three times, respectively. The crack elongation in the longitudinal direction occurred 5.8 times with time. Together, within the time of 3.5 ms, the equivalent stresses increased twice, after which the growth of the crack stopped due to the gas decompression. Moreover, studies on the growth of the crack-like defect in its tip area at the maximum pressure showed that additional considerations on the pressure on the crack edges led to an increment of 3.6% of the crack length. The results of this work can be used for the development of measurements for operating gas pipelines in the field of structural reinforcement.

Exploring localized ENZ resonances and their role in superscattering, wideband invisibility, and tunable scattering

While the role and manifestations of the localized surface plasmon resonances (LSPRs) in anomalous scattering, like superscattering and invisibility, are quite well explored, the existence, appearance, and possible contribution of localized epsilon-near-zero (ENZ) resonances still invoke careful exploration. In this paper, that is done along with a comparison of the resonances of two types in the case of thin-wall cylinders made of lossy and loss-compensated dispersive materials. It is shown that the localized ENZ resonances exist and appear very close to the zero-permittivity regime, i.e., at near-zero but yet negative permittivity that is similar to the ENZ modes in thin planar films. Near- and far-field characteristics of the superscattering modes are investigated. The results indicate that the scattering regimes arising due to LSPRs and localized ENZ resonances are distinguishable in terms of the basic field features inside and around the scatterer and differ in their contribution to the resulting scattering mechanism, e.g., in terms of the occupied frequency and permittivity ranges as well as the sensitivity to the wall thickness variations. When the losses are either weak or tend to zero due to the doping with gain enabling impurities, the sharp peaks of the scattering cross-section that are yielded by the resonances can be said to be embedded into the otherwise wide invisibility range. In the case of lossy material, a wide and continuous invisibility range is shown to appear not only due to a small total volume of the scatterer in the nonresonant regime, but also because high-Q superscattering modes are suppressed by the losses. For numerical demonstration, indium antimonide, a natural lossy material, and a hypothetical, properly doped material with the same real part of the permittivity but lower or zero losses are considered. In the latter case, variations of permittivity with a control parameter can be adjusted in such a way that transitions from one superscattering mode to another can be achieved. In turn, transition from the strong-scattering to the invisibility regime is possible even for the original lossy material. The basic properties of the studied superscattering modes may be replicable in artificial structures comprising natural low-loss materials.

Achieving synchronous compression-shear loading on SHPB by utilizing mechanical metamaterial

Materials in service often experience complex stress states, such as a combination of shear and compression or tension. Therefore, it is crucial to experimentally measure the mechanical responses of materials under complex stress states before designing structures, as these responses differ from those under uniaxial loading. However, conducting combined loading experiments, especially under dynamic impact, is challenging and usually requires complex and costly equipment. In the present work, by employing compression-torsion coupling metamaterials, an easy method is proposed for the first time to achieve synchronous dynamic compression-shear loading on 1D Split Hopkinson Pression Bar (SHPB), which is also feasible for quasi-static experiments on universal material testing machine. The compression-torsion coupling metamaterial can convert a compression wave into combined waves of compression and torsion, and ensures the two waves naturally synchronously act on the thin-walled cylinder specimen. Since the compression-shear dynamic loading experiment can be performed on a traditional 1-D SHPB, it is a cost-effective, convenient, and easily implementable method. Both the dynamic and quasi-static mechanical properties of 1060 Al were measured under various shear-compression ratios, and a well von-Mises yield surface was obtained with strain rate insensitivity, confirming the validity of the proposed experimental methods.

Mehaničko modeliranje termomehaničkih procesa

The problem of stress in perforated thin-walled cylinders due to mechanical and thermal load was analyzed for cases where the load of the system varies both along the cylinder circumference and axially. Starting from the solution and considerations for a smooth thin-walled cylinder, the concept was expanded and the distribution of deformations caused by thermal loads on the cylinder and the resulting stresses in the structure of the thin-walled perforated cylinder was observed for a specific form of perforation. The cylindrical perforated burner is one of the main elements of premixed condensing boiler for home heating systems. The quality of combustion, and thus the heat load on the outer sheath of the burner, largely depends on the layout, shape and dimensions of the perforation. This paper presents the mechanical modeling of thermomechanical processes of a cylindrical gas burner with premixing for a triangular layout or the so-called checkerboard shape of perforation.

Study on post-buckling crack propagation in thin-walled cylinders under dynamic cyclic load

Study on post-buckling crack propagation in thin-walled cylinders under dynamic cyclic load

Necking of thin-walled cylinders via bifurcation of incompressible nonlinear elastic solids.

Necking localization under quasi-static uniaxial tension is experimentally observed in ductile thin-walled cylindrical tubes, made of soft polypropylene. Necking nucleates at multiple locations along the tube and spreads throughout, involving the occurrence of higher-order modes, evidencing trefoil and fourth-foiled (but rarely even fifth-foiled) shaped cross-sections. No evidence of such a complicated necking occurrence and growth was found in other ductile materials for thin-walled cylinders under quasi-static loading. With the aim of modelling this phenomenon, as well as all other possible bifurcations, a two-dimensional formulation is introduced, in which only the mean surface of the tube is considered, paralleling the celebrated Flügge 's treatment of axially-compressed cylindrical shells. This treatment is extended to include tension and a broad class of nonlinear-hyperelastic constitutive law for the material, which is also assumed to be incompressible. The theoretical framework leads to a number of new results, not only for tensile axial force (where necking is modelled and, as a particular case, the classic Considère formula is shown to represent the limit of very thin tubes), but also for compressive force, providing closed-form formulae for wrinkling (showing that a direct application of the Flügge equation can be incorrect) and for Euler buckling. It is shown that the J2-deformation theory of plasticity (the simplest constitutive assumption to mimic through nonlinear elasticity the plastic branch of a material) captures multiple necking and occurrence of higher-order modes, so that experiments are explained. The presented results are important for several applications, ranging from aerospace and automotive engineering to the vascular mechanobiology, where a thin-walled tube (for instance an artery, or a catheter, or a stent) may become unstable not only in compression, but also in tension.

Energy analysis of vibratory penetration of large-scale steel cylinders

Vibratory penetration was successfully used to install 120 integral thin-walled steel cylinders 22 m in diameter in the Hong Kong-Zhuhai-Macao Bridge. However, the eight-hammer group was found overpowered at the western island and underpowered at the eastern site due to insufficient understanding of the mechanisms of vibratory piling. In this study, energy analysis was conducted to reveal the energy characteristics of vibratory penetration, including the periodical energy superposition along the cylinder shaft, the continuous energy consumption in the soil, and the dynamic equilibrium of the total energy. The influences of vibratory soil resistance and loading frequency on the energy distributions have been thoroughly discussed. In contrast to the notion that larger input energy leads to a faster penetration, it is revealed that the vibratory penetration velocity positively correlates to the energy stored in the cylinder, the ratio of kinetic to strain energy, and the characteristic frequencies of the soil-pile system. The actual output power of the vibratory motors is influenced by the vibratory force, the ultimate soil resistance, and the soil mobilization degree. The vibration frequency is optimized as 31.1 Hz for Cylinder E9 and 15 Hz for Cylinder W36 to ensure efficiency and safety.